Trigonometric Functions
posted by Mike on .
Determine the Value of all six trigonometric functions of theta when given?
I need help. This is for my midterm review, if anyone is willing to help, I'd appreciate it.
a) sin theta= 3/5 and theta is in quadrant 1.
b) tan theta= 2 and theta is in quadrant II
c) sec theta = 2 radical 3/3 and theta is in quadrant II
d) csc theta= 2/3 and theta is in quadrant III.
I need to find all six trigonometric functions for each one ( sin, cos, tan, csc, sec, cot)

With each function given, you have two sides of a right triangle. Using the pyth theorm, you can find the other side, and thus, the other functions. We will be happy to check your work.
For example, c) If secTheta = 2 sqrt (1/3), then the sides of the triangle are
opposite figure out
adjacent sqrt 3
hypo= 2
and the opposite will be
4=3+opposite^2 or opposite is +1, Now in quadrant two, that means sec is negative, so it should have been 2sqrt(1/3), and the opposite (vertical) is 1. From that you get the six functions. 
I will do c. You try the rest.
Oh no I won't > sign of sec is negative in quad 2. I think typo
I will do d.
d) csc T = 1/sin T = 2/3
Hey! what is going on here?
the absolute value of sin T may not be greater than 1. It can not be 3/2
Either we are looking at typos or someone is playing games with you.
I will do b I guess
b) draw triangle in quad 2
1 along x axis
+2 up at x = 2
now hypotenuse = sqrt (1^2 + 2^2) = sqrt 5
so
sin = 2/sqrt 5
cos = 1/sqrt 5 = (1/5)sqrt 5
tan = 2/1
csc = 1/sin = (1/2)sqrt 5
sec = 1/cos = sqrt 5
cot = 1/tan = 1/2 
prove the identities (theta + phi), cos theta = 1/3 in Quadrant III, sin theta = 1/4 in quadrant II